Engineering / advanced
Analyze programs before compiling tensors
Track graph capture, intermediate representations, symbolic shapes, effects, aliasing, and guards to establish which tensor transformations are valid.
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Module 01 advanced
Analyze programs before compiling tensors
Track graph capture, intermediate representations, symbolic shapes, effects, aliasing, and guards to establish which tensor transformations are valid.
- 01
Capture a tensor region without confusing it with the whole program
Separate tracing, guarded reuse, eager execution, and ahead-of-time export using a small inference pipeline and an explicit compilation budget.
27 min - 02
Give every tensor value one definition while tracking storage separately
Read SSA definitions, predecessor-selected values, dominance, and tensor-versus-buffer semantics without treating unique names as proof of non-aliasing.
27 min - 03
Treat symbolic dimensions as a domain with obligations
Propagate two-dimensional tensor shapes, preserve element counts, and distinguish mathematically valid constraints from what a compiler can establish.
27 min - 04
Guard every assumption that changes indexing or semantics
Derive a stride counterexample and connect artifact dispatch to shape, layout, dtype, device, and explicitly specialized values.
27 min - 05
Preserve reads of shared storage across tensor updates
Analyze two-dimensional views, read-after-write dependencies, functionalization, and safe buffer reuse using a concrete mutation counterexample.
27 min - 06
Order observable effects even when tensor values are independent
Separate value dependencies, mutable state, pseudorandom keys, I/O, and speculation safety when deciding which operations may move or repeat.
27 min - 07
Fold what is known without inventing algebraic permission
Distinguish compile-time constants from dynamic inputs and preserve specified floating-point semantics when simplifying a partially evaluated tensor program.
27 min - 08
Measure the boundary instead of declaring every graph break a failure
Account for compilation, eager regions, dispatch, synchronization, and fusion limits using a fictional pipeline and a synthetic roofline ceiling.
27 min - 09
Transform the derivative graph with shapes and saved values intact
Read reverse-mode tensor IR as a shape-aware program transformation, preserving cotangent accumulation, broadcasts, residuals, and effects.
27 min - 10
Validate the analyzed domain, not just one compiled answer
Combine structural verification, guard-negative fixtures, differential oracles, floating-point tolerances, and bounded proof claims in a compiler validation plan.
27 min